Algebra Examples

$\frac{a x + b}{c} - d = e$

Step 1

Simplify $\frac{a x + b}{c} - d$ .

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Step 1.1

To write $- d$ as a fraction with a common denominator, multiply by $\frac{c}{c}$ .

$\frac{a x + b}{c} - d \cdot \frac{c}{c} = e$

Step 1.2

Combine $- d$ and $\frac{c}{c}$ .

$\frac{a x + b}{c} + \frac{- d c}{c} = e$

Step 1.3

Combine the numerators over the common denominator.

$\frac{a x + b - d c}{c} = e$

Step 2

Multiply both sides by $c$ .

$\frac{a x + b - d c}{c} c = e c$

Step 3

Simplify the left side.

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Step 3.1

Simplify $\frac{a x + b - d c}{c} c$ .

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Step 3.1.1

Cancel the common factor of $c$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{a x + b - d c}{c} c = e c$

Step 3.1.1.2

Rewrite the expression.

$a x + b - d c = e c$

Step 3.1.2

Reorder.

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Step 3.1.2.1

Move $d$ .

$a x + b - 1 c d = e c$

Step 3.1.2.2

Move $b$ .

$a x - 1 c d + b = e c$

Step 4

Solve for $x$ .

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Step 4.1

Rewrite $- 1 c$ as $- c$ .

$a x - c d + b = e c$

Step 4.2

Move all terms not containing $x$ to the right side of the equation.

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Step 4.2.1

Add $c d$ to both sides of the equation.

$a x + b = e c + c d$

Step 4.2.2

Subtract $b$ from both sides of the equation.

$a x = e c + c d - b$

Step 4.3

Divide each term in $a x = e c + c d - b$ by $a$ and simplify.

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Step 4.3.1

Divide each term in $a x = e c + c d - b$ by $a$ .

$\frac{a x}{a} = \frac{e c}{a} + \frac{c d}{a} + \frac{- b}{a}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $a$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{a x}{a} = \frac{e c}{a} + \frac{c d}{a} + \frac{- b}{a}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{e c}{a} + \frac{c d}{a} + \frac{- b}{a}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Move the negative in front of the fraction.

$x = \frac{e c}{a} + \frac{c d}{a} - \frac{b}{a}$